Simplify the following expression: $\dfrac{80a^2}{32a^2}$ You can assume $a \neq 0$.
Solution: $ \dfrac{80a^2}{32a^2} = \dfrac{80}{32} \cdot \dfrac{a^2}{a^2} $ To simplify $\frac{80}{32}$ , find the greatest common factor (GCD) of $80$ and $32$ $80 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5$ $32 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$ $ \mbox{GCD}(80, 32) = 2 \cdot 2 \cdot 2 \cdot 2 = 16 $ $ \dfrac{80}{32} \cdot \dfrac{a^2}{a^2} = \dfrac{16 \cdot 5}{16 \cdot 2} \cdot \dfrac{a^2}{a^2} $ $\phantom{ \dfrac{80}{32} \cdot \dfrac{2}{2}} = \dfrac{5}{2} \cdot \dfrac{a^2}{a^2} $ $ \dfrac{a^2}{a^2} = \dfrac{a \cdot a}{a \cdot a} = 1 $ $ \dfrac{5}{2} \cdot 1 = \dfrac{5}{2} $